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 Science > Math > Number Theory > Elliptic Curves and Modular Forms

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Science > Math > Number Theory > Elliptic Curves and Modular Forms

Elliptic Curves and Modular Forms:

Arithmetic of Cuves

Papers and surveys by Ed Schaefer.

http://math.scu.edu/~eschaefe/nt.html

Bibliography for Automorphic and Modular Forms, L-Functions, Representations, and Number Theory

Compiled by Paul Garrett, 1996.

http://www.math.umn.edu/~garrett/m/b/bib.html

The Birch and Swinnerton-Dyer Conjecture

A Clay Mathematics Institute Prize problem, with description by Andrew Wiles [PDF] and lecture by Fernando Rodriguez-Villegas [.ram].

http://www.claymath.org/millennium/Birch_and_Swinnerton-Dyer_Conjecture/

Graand

Free Classified Ads Portal

www.graand.com

Counting Points on Elliptic Curves

Robert Harley, Pierrick Gaudry, François Morain and Mireille Fouquet have established new records for point counting in characteristic 2, using a new algorithm by to Takakazu Satoh.

http://www.math.jussieu.fr/~fouquet/elliptic.html

Course Notes

Full notes as .dvi, .pdf, and .ps files for all the advanced courses J. S. Milne taught between 1986 and 1999.

http://www.jmilne.org/math/CourseNotes/

ECDL Project

Elliptic Curve Discrete Logarithms Project. They solved ECC2K-108 in April 2000. History and related papers.

http://pauillac.inria.fr/~harley/ecdl/

ECMNET

The ECMNET Project to find large factors by the Elliptic Curve Method, mainly Cunningham numbers.

http://www.loria.fr/~zimmerma/records/ecmnet.html

An Elementary Introduction to Elliptic Curves

By Len Charlap, David Robbins and Raymond Coley. Downloadable text in PostScript (.ps) format.

http://www.idaccr.org/reports/reports.html

Elliptic Curves

Links to research papers maintained by Stéfane Fermigier.

http://www.fermigier.com/fermigier/elliptic.html.en

Elliptic Curves and Cryptology

Marc Joye's list of elliptic curve resources includes people, books, and links. Many preprints are available from the site.

http://www.geocities.com/marcjoye/biblio_ell.html

Elliptic Curves and Elliptic Functions

Introductory notes by Charles Daney.

http://cgd.best.vwh.net/home/flt/flt03.htm

Elliptic Curves and Formal Groups

Lecture notes from a seminar J. Lubin, J.-P. Serre and J. Tate.

http://www.ma.utexas.edu/users/voloch/lst.html

Elliptic Curves and Modular Forms

Slides (GIF) of lectures by Karl Rubin at Stanford University.

http://math.stanford.edu/~rubin/lectures/sumo/

Elliptic Curves and Their Applications to Cryptography

Web text by Andreas Enge.

http://www.lix.polytechnique.fr/Labo/Andreas.Enge/buch/buch/buch.html

Elliptic Curves Handout

Syllabus and detailed reading list by Miles Reid, University of Warwick.

http://www.maths.warwick.ac.uk/~miles/MA426/

Elliptic Curves II

Lecture notes by Johan P. Hansen.

http://home.imf.au.dk/matjph/Ell-E99.html

Elliptic Curves with H. A. Verrill

Lecture notes and resources by Helena Verrill, Louisiana State University, 2004.

http://www.math.lsu.edu/~verrill/teaching/math7280/index.html

Elliptic Divisibility Sequences

Articles and links, compiled by Graham Everest.

http://www.mth.uea.ac.uk/~h090/EDS.html

Elliptic Functions and Elliptic Curves

Lecture notes by Jan Nekovář (PS/PDF).

http://www.math.jussieu.fr/~nekovar/co/ln/el/

Elliptical Curve Cryptography

Explains the difference between an elliptical curve and an ellipse. Discusses fields, applications, choosing a fixed point, and related topics.

http://www.cryptoman.com/elliptic.htm

Explicit Approaches to Modular Abelian Varieties

William Stein, Ph.D. thesis, Berkeley, 2000.

http://modular.fas.harvard.edu/papers/explicit/

14H52: Elliptic Curves

From the Known Math series.

http://www.math.niu.edu/~rusin/known-math/index/14H52.html

History of Elliptic Curve Rank Records

A table up to rank 24 compiled by Andrej Dujella.

http://www.math.hr/~duje/tors/rankhist.html

Iwasawa Theory of Elliptic Curves

Lecture notes and surveys by Ralph Greenberg, University of Washington (PS).

http://www.math.washington.edu/~greenber/research.html

Joseph Silverman

Includes errata for his books Rational Points on Elliptic Curves and Advanced Topics in the Arithmetic of Elliptic Curves.

http://www.math.brown.edu/~jhs/

Kolyvagin Seminar

A semester-long seminar studying Kolyvagin's application of Euler systems to elliptic curves. Includes extensive lecture notes in PostScript or DVI format.

http://math.berkeley.edu/~osserman/seminar/

Mathematical Things

Tom Womack's pages address many elliptic curve subjects, including curves of given rank and small conductor, Mordell curves of large rank, and interesting torsion groups.

http://tom.womack.net/maths/maths.htm

Modular Forms and Hecke Operators

Notes by William A. Stein of a course by Ken Ribet.

http://modular.fas.harvard.edu/MF.html

Modular Forms Course

Notes of a 1996 Berkeley course of Ken Ribet's on modular forms and Hecke operators.

http://modular.fas.harvard.edu/Tables/Notes/

On 5 and 7 Descents for Elliptic Curves

Tom Fisher's Ph.D. thesis (Cambridge, 2000) in DVI and PS format.

http://www.dpmms.cam.ac.uk/~taf1000/thesis.html

Papers by Richard Borcherds

Including proof of the Moonshine Conjecture (TeX,DVI,PDF).

http://math.berkeley.edu/~reb/papers/

Prime Values of Elliptic Divisibility Sequences

By Graham Everest.

http://www.mth.uea.ac.uk/~h090/primeEDS.html

A Proof of the Full Shimura-Taniyama-Weil Conjecture

Article by Henri Darmon on the completion of the proof by Wiles, Breuil, Conrad, Diamond and Taylor. [PDF]

http://www.ams.org/notices/199911/comm-darmon.pdf

Rational Points on Elliptic Curves

A course by Jerrold Tunnell. An introduction to rational points on elliptic curves through examples.

http://www.math.rutgers.edu/~tunnell/math574.html

Recent Progress in the Theory of Elliptic Curves

An abstract to Henri Darmon's and Bertolini's work, which approaches a p-adic variant of the Birch - Swinnerton-Dyer conjecture, for curves of rank higher than one.

http://www.cms.math.ca/CMS/Events/winter98/w98-abs/node2.html

Richard Taylor

Publications including the joint paper with Andrew Wiles which completed the proof of Fermat's Last Theorem.

http://www.math.harvard.edu/~rtaylor/

Torsion Points on Elliptic Curves

Elementary introduction and brief explanation of some well-known results.

http://mat.uab.cat/~xarles/elliptic.html